Thermal Spreading Resistance of Eccentric Heat Sources on Rectangular Flux Channels

2003 ◽  
Vol 125 (2) ◽  
pp. 178-185 ◽  
Author(s):  
Y. S. Muzychka ◽  
J. R. Culham ◽  
M. M. Yovanovich
Keyword(s):  
General Solution ◽  
Separation Of Variables ◽  
Heat Sources ◽  
Spreading Resistance ◽  
Discrete Heat Sources ◽  
Special Cases ◽  
Separation Of Variables Method

A general solution, based on the separation of variables method for thermal spreading resistances of eccentric heat sources on a rectangular flux channel is presented. Solutions are obtained for both isotropic and compound flux channels. The general solution can also be used to model any number of discrete heat sources on a compound or isotropic flux channel using superposition. Several special cases involving single and multiple heat sources are presented.

Thermal Spreading Resistance of Eccentric Heat Sources on Rectangular Flux Channels

2000 ◽  
Author(s):  
Y. S. Muzychka ◽  
J. R. Culham ◽  
M. M. Yovanovich
Keyword(s):  
General Solution ◽  
Separation Of Variables ◽  
Heat Sources ◽  
Spreading Resistance ◽  
Discrete Heat Sources ◽  
Special Cases ◽  
Separation Of Variables Method

Abstract A general solution, based on separation of variables method for thermal spreading resistances of eccentric heat sources on a rectangular flux channel is presented. Solutions are obtained for both isotropic and compound flux channels. The general solution can also be used to model any number of discrete heat sources on a compound or isotropic flux channel using superposition. Several special cases involving a single and multiple heat sources are presented.

scholarly journals Conformable Derivatives in Laplace Equation and Fractional Fourier Series Solution

2019 ◽  
Vol 9 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Ronak Pashaei ◽  
Mohammad Sadegh Asgari ◽  
Amir Pishkoo
Keyword(s):  
Fourier Series ◽  
Laplace Equation ◽  
Series Solution ◽  
Fractional Integral ◽  
Fourier Coefficients ◽  
Separation Of Variables ◽  
Special Cases ◽  
Separation Of Variables Method ◽  
Conformable Derivatives ◽  
Conformable Fractional Integral

In this paper the solution of conformable Laplace equation, \frac{\partial^{\alpha}u(x,y)}{\partial x^{\alpha}}+ \frac{\partial^{\alpha}u(x,y)}{\partial y^{\alpha}}=0, where 1 < α ≤ 2 has been deduced by using fractional fourier series and separation of variables method. For special cases α =2 (Laplace's equation), α=1.9, and α=1.8 conformable fractional fourier coefficients have been calculated. To calculate coefficients, integrals are of type "conformable fractional integral".

Thermal Resistances of Circular Source on Finite Circular Cylinder With Side and End Cooling

2003 ◽  
Vol 125 (2) ◽  
pp. 169-177 ◽  
Author(s):  
M. M. Yovanovich
Keyword(s):  
General Solution ◽  
Circular Cylinder ◽  
Circular Disk ◽  
Spreading Resistance ◽  
Pin Fin ◽  
Special Cases ◽  
Extended Surface ◽  
The One ◽  
Circular Source ◽  
Special Case

General solution for thermal spreading and system resistances of a circular source on a finite circular cylinder with uniform side and end cooling is presented. The solution is applicable for a general axisymmetric heat flux distribution which reduces to three important distributions including isoflux and equivalent isothermal flux distributions. The dimensionless system resistance depends on four dimensionless system parameters. It is shown that several special cases presented by many researchers arise directly from the general solution. Tabulated values and correlation equations are presented for several cases where the system resistance depends on one system parameter only. When the cylinder sides are adiabatic, the system resistance is equal to the one-dimensional resistance plus the spreading resistance. When the cylinder is very long and side cooling is small, the general relationship reduces to the case of an extended surface (pin fin) with end cooling and spreading resistance at the base. The special case of an equivalent isothermal circular source on a very thin infinite circular disk is presented.

scholarly journals Water entry of an expanding wedge/plate with flow detachment

2016 ◽  
Vol 797 ◽  
pp. 322-344 ◽  
Author(s):  
Yuriy A. Semenov ◽  
Guo Xiong Wu
Keyword(s):  
Free Surface ◽  
General Solution ◽  
Water Entry ◽  
Hodograph Method ◽  
Fixed Length ◽  
Pressure Distributions ◽  
Initial Stage ◽  
Special Cases ◽  
Wedge Plate ◽  
Special Case

A general similarity solution for water-entry problems of a wedge with its inner angle fixed and its sides in expansion is obtained with flow detachment, in which the speed of expansion is a free parameter. The known solutions for a wedge of a fixed length at the initial stage of water entry without flow detachment and at the final stage corresponding to Helmholtz flow are obtained as two special cases, at some finite and zero expansion speeds, respectively. An expanding horizontal plate impacting a flat free surface is considered as the special case of the general solution for a wedge inner angle equal to ${\rm\pi}$. An initial impulse solution for a plate of a fixed length is obtained as the special case of the present formulation. The general solution is obtained in the form of integral equations using the integral hodograph method. The results are presented in terms of free-surface shapes, streamlines and pressure distributions.

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